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Old, good and useful temperaments
24 harmonics
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IN TUNINGLAND
When we play with pure intervals, the tuning problems moves to the chord changes,
The purer, the larger the "comma shift" is needed to hold the pitch. That means two or more pitches of the same tone.
As shown in the introduction, it is not possible to play C-dm-G-C purely.
If we do we will fall (click) in pitch.
To avoid this you either have to make a tuning compromise, of which there are inexorable many, and one you use all the time (ET). Or you have to adjust single tones. Have 2 or more pitches of the same tone.
Like here (click and hear ), the distance becomes too big between the two D.
And the G does not fit this fifth: low D to A, so Dsus4 is also quite impossible to use.
I transfer this setup above identically, but now with Bb (click and hear) as a starting point.
Of course, this does not work alone, but the advantages and disadvantages are different in the two.
And that is the point !
Play both a couple of times and compare.
My idea has been to halve this comma shift, then all the tones are adjusted but not so much.
Bb+1 infiltrates into C0.
Some tones are higher in Bb+1 such as F, Bb, D, A, F #
While others are lower like C, G, E, B
The interesting thing about the idea is that D from Bb+1 lies midway between the two D`s in C0.
Bb+1, in turn, has two C`s at a intolerable distance. And C from C0 lies midway between these.
So they are as mentioned infiltrated into each other !
So let us hear how IN TUNINGLAND handle this problem.
Click and hear
One challenge is to play with two keys of the 2. tone in the scale. (high D in C0 is on the D# key)
Those setups of the same color are related, while switching to the opposite color halves the comma.
User Scale:
07 provides Gb-dur setup (Gb+3) with an additional Ab on the A key
08 provides Ab-Dur setup (Ab+2) with an additional Bb on the B key.
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This is the main setup :
09 provides Bb duration setup (Bb+1) with an additional C on the C # key
10 provides C major setup (C0) with an additional D on the D # key.
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11 provides the D major setup (D-1) with an additional E on the F key
12 provides E-major setup (E-2) with an additional F # on the G key
13 provides F # door setup (F#-3) with an additional G # on the A key.
It is C0 and Bb+1 (10 and 09) that hold the main idea, the others are an extension towards other keys.
The reds are in common tuning level and therefore C0 and Ab+2 contain some chords that are exactly the same. While some chords represent an extension of the chord possibilities
While different colors will say that the tuning level is different and can`t be overdubbed. Some tones are higher and some lower between them.
IT 0 provides perfectly pure thirds and fifths, but maybe a too annoying comma shift.
IT-2 provides perfectly pure thirds and fifths as in the normal piano tuning (equal) , but a comma shift that is easily tolerated. (-2 stands for 2 cents narrowed fifths)
IT -1 gives perfectly pure thirds and fifths between pure and as in Equal T , and a comma shift between IT0 and IT -2.
This is my favourite!
Here (click)is the overview of where the chords are in the different setups.
Here is an example (click and hear) for organ .
(And here is another example with my way of showing the relations between the tones.)
Hope you get curious about the idea and have some good moments with beautiful pure chords!
Link to the other tunings :
Old, good and useful temperaments
24 harmonics
User Scales to Kronos (Remember to save your own Global setting)
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